Sentence examples for counting measure from inspiring English sources

We use the inequalities (1.7), (1.8), and Theorem 1.2 with counting measure.

If (Omega= mathbb {Z}_) and μ is the counting measure, we obtain a simple sufficient condition for the Fatou inequality: Suppose that (Omega= mathbb {Z}_) and that μ is the counting measure.

Assume ( C 1 1 )-( C 4 1 ), and suppose μ is the counting measure on P ( X ), that is, μ u : = 1 for all u ∈ X.

The paper deals with l1-multipliers, where X= G is a discrete (countable) solvable group with ∀x∈G, x4= 1, μ is the counting measure andTΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ="Φ∗ is a l1(G) function, suppΦ generates G.

Then ∥ f ∥ BMO L p, q ( X ) ∼ inf θ sup τ μ − 1 s 1 ∥ f − θ τ − 1 ∥ L r, s ( X ), where 'sup' is taken over all stopping times τ and 'inf' is taken over all adapted process θ = n ≥ 0. Definition 2.1 Let ν be a nonnegative measure on Ω × N, where N is equipped with the counting measure dm.

Denote by N ( d t, d v ) the Poisson counting measure associated with p, that is, N ( t, Z ) = ∑ s ∈ D p, s ≤ t I Z ( p ( s ) ) with a measurable set Z ∈ B ( Y − { 0 } ), which denotes the Borel σ-field of Y − { 0 }.

They are relentlessly numerical, devoted perhaps first of all to the project of counting, measuring and listing.

In Santa Monica, with very few ballots counted, Measure LV was lagging.

Finally, marker gene counts measure organism frequency rather than genomic DNA content, which is measured by the above tools.

Fries were counted, measured (total length), and weighed.

Either the variance among bin counts, or an entropy associated with the bin counts, measures the progress of mixing.